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Properties

Label 2475.4.fj
Level $2475$
Weight $4$
Character orbit 2475.fj
Rep. character $\chi_{2475}(131,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $8608$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2475.fj (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2475 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2475, [\chi])\).

Total New Old
Modular forms 8672 8672 0
Cusp forms 8608 8608 0
Eisenstein series 64 64 0

Trace form

\( 8608 q - 16 q^{3} + 4282 q^{4} - 72 q^{5} - 44 q^{9} + O(q^{10}) \) \( 8608 q - 16 q^{3} + 4282 q^{4} - 72 q^{5} - 44 q^{9} - 9 q^{11} - 56 q^{12} - 18 q^{14} + 110 q^{15} + 17050 q^{16} - 264 q^{20} - 35 q^{22} - 18 q^{23} + 280 q^{25} - 604 q^{27} + 30 q^{31} - 228 q^{33} + 26 q^{34} + 804 q^{36} + 120 q^{37} + 30 q^{38} - 3664 q^{42} - 308 q^{45} - 2346 q^{47} - 520 q^{48} + 206176 q^{49} + 846 q^{55} - 6288 q^{56} - 1078 q^{58} + 1476 q^{59} + 3266 q^{60} - 134584 q^{64} - 3654 q^{66} + 912 q^{67} + 496 q^{69} + 2964 q^{70} + 5144 q^{75} - 8121 q^{77} + 616 q^{78} - 1484 q^{81} - 128 q^{82} - 18 q^{86} - 1307 q^{88} - 4140 q^{91} + 18810 q^{92} + 12980 q^{93} + 1146 q^{97} + 218 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2475, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.